Study on optimization of engineering parameters for medium-deep U-shaped geothermal wells based on indoor physical model tests

Deep-buried U-shaped geothermal wells (DBUSWs) are closed-loop systems that extract heat without groundwater production, yet predicting their subsurface heat-transfer behavior remains challenging, and key design parameters are poorly constrained. This study develops a similarity-based indoor physical model for the horizontal section of a medium-to-deep DBUSW and conducts sensitivity analyses of injection flow rate, injection temperature, continuous operation time, and terrestrial heat flow. Injection flow rate and injection temperature mainly affect the toe (outlet) temperature within a single operating cycle and have limited influence on the surrounding-rock disturbance extent under calibrated conditions. In contrast, longer continuous operation enlarges the thermal-disturbance radius and reduces the initial outlet temperature of the next cycle because shut-in recovery becomes insufficient. Terrestrial heat flow governs recovery during shut-in; a threshold of about 200 mW/m2 distinguishes near-complete recovery from persistent cooling under a 6-month on/6-month off cycle. Across tested conditions, heat transfer approaches a quasi-steady state at 550–600 m, suggesting an optimal horizontal length of 600 m. For average terrestrial heat-flow conditions in China, recommended ranges are 8.7–14°C injection temperature, 4–5 months continuous operation, and 26–35 m3/h injection flow rate.